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Unformatted text preview: Homework Set No. 2, Physics 880.08 Deadline Wednesday, November 3, 2010 1. (10 pts) In class we showed that Dirac spinors transform as D ( x ) D ( x ) = parenleftBigg e i 2 vector ( vector + i vector ) e i 2 vector ( vector i vector ) parenrightBigg D ( x ) (1) under Lorentz transformations. Show that this transformation rule is equivalent to D ( x ) D ( x ) = e i 4 D ( x ) where = i 2 [ , ] . As usual i = i and i = 1 2 ijk jk . You may consider boosts and rotations separately for the full credit. 2. (a) (5 pts) Complete the proof started in class that is a 4-vector by showing that it transforms like one under infinitesimal boosts. is the Dirac spinor which transforms according to Eq. (1). (b) (5 pts) Prove that 5 is a 4-vector under both boosts and rotations. What happens to it under parity?...
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